Question

The path of the earth around the sun is an ellipse with the sun at one focus. The ellipse has a major axis of 186,000,000 miles and eccentricity of 0.017. Find the distance between the earth and the sun when the earth is (a) closest to the sun and (b) farthest from the sun

Answer 1

a)
`r = 182838000\,mi`, b)
`r = 189162000\,mi`

Step-by-step explanation:

a) The distance between the center and one of the foci is:

`c = \epsilon \cdot a`

`c = (0.017)\cdot (186000000\,mi)`

`c = 3162000\,mi`

The shortest distance is:

`r = a - c`

`r = 186000000\,mi -3162000\,mi`

`r = 182838000\,mi`

b) The longest distance is:

`r = a + c`

`r = 186000000\,mi +3162000\,mi`

`r = 189162000\,mi`